Anomalous behavior of the $E_{u}^{1}$ infrared-active phonon mode in Bi$_{2-x}$Sr$_x$Se$_3$ crystal

We have studied spectral evolution of the $E_{u}^{1}$ phonon line of a topological insulator Bi$_{2-x}$Sr$_x$Se$_3$ with temperature. Unlike the Raman-active phonons, the $E_{u}^{1}$ mode demonstrates softening upon cooling the crystal, and the corresponding spectral line acquires a pronounced Fano-like shape at temperatures $T\lesssim100$ K. We interpret the latter effect as a signature of specific coupling of the bulk infrared active phonons to surface Dirac electrons. Using coherent resonant excitation of the $E_{u}^{1}$ mode as a surface sensitive tool, we have detected softening of the surface counterpart of the bulk $E_{u}^{1}$ phonon mode upon strontium doping. This observation can be an evidence of enhanced electron–phonon interaction at the surface of the Bi$_{2-x}$Sr$_x$Se$_3$ crystal.